Lurchers - yes, good post.
I think that archaeology is a very interesting one - I'm not sure if I would describe it as a science as such, although scientific processes happen in the process of archaeology. My only real knowledge of archaeology is to do with the places in the Bible, which of course are loaded with religious, political and socio-economic significance, so, for example access to what might be validly thought of as archaeological sites is fraught with difficulty (The Temple Mount in Jerusalem is an obvious example of this: deeply problematic) So archaeological activity is determined by political, religious and socio-economic factors from the outset.
Without going on too much, the approaches to the archaeology of this region have varied massively over the years - the 'Bible and spade' school of 'Biblical archaeology' was made up of people who, maybe literally, had a Bible in one hand and a spade in the other, went to the places named in the Bible and dug. Problem is that it's not always very clear where some of the places named in the Bible actually are - classic example is the route of the Exodus - is it northerly or southerly? We just don't know.
To make things more complex, are the numbers in the Bible supposed to be taken literally or not? (I'd say not, personally). Biblical literalism is a big issue in the archaeology of that area. So if the Exodus was a huge train of thousands as in the movies, that'd suggest a very different archaeological imprint from a 'small group of runaway slaves' suggested by a leading Jewish scholar. So a) we don't always know where to look, and b) we don't always know what we are looking for.
More complex still, the digs are v. expensive and are often funded by religious groups with a very deeply vested interest in the results. Very sadly of course, this a beleagured and war torn part of the world, and that has a devastating effect on its archaeological heritage - Syria's very ancient sites are being decimated :( so very sad
Finally, there's the issue of interpretation. We find something, and we assess what it is, what it was used for, when it dates to, and so on. We use our historical knowledge to do that. So historical interpretation and archaeological interpretation go hand in hand. If you believe, like one major Israeli archaeologist does, that King David never existed, you're not going to go looking for evidence of David's palace in Jerusalem. Or rather, if you find something that might be a palace, you're not going to assign it to David. www.timesofisrael.com/archaeologists-say-one-of-king-davids-palaces-found/ this is interesting; read the very last para.
So all in all it's a highly subjective process. There are still huge areas of the middle east that have not been excavated, there are others that have been done to death, there are very significant areas that have been wrecked by war (Syria was incredibly important in early Christianity). This all means, IMO, that it's a fascinating and truly worthwhile enterprise, but can't be the be-all and end-all of truth -finding - I don't think it's reasonable to say, for example, that archaeology has disproved the Exodus. (Some people do say that.)